Finite Group Databasebeta

← Group #11721563

Character table — Group #11721563

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size12336669991233666999246612121218181824661212121818182466121212181818481212242424363636481212242424363636
order13333332662666666266412121212121241212824242424242482424824242424242482424412121212121241212412121212121241212
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-1
χ311−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ411−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32
χ511−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ611−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32
χ72222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-1000
χ822−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i32000
χ922−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i32000
χ106-3000000006-3000000006-3000000006-3000000006-3000000006-3000000006-300000000
χ1111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ121111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111
χ1311−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i32
χ1411−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32
χ1511−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i32
χ1611−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32
χ172222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-10002222-1-1-1000-2-2-2-2111000-2-2-2-2111000
χ1822−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i32000
χ1922−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i32000
χ206-3000000006-3000000006-3000000006-3000000006-300000000-6300000000-6300000000
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ221111111-1-1-11111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111
χ2311−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321+i32-11−i321+i32-11−i321+i32
χ2411−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32
χ2511−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321−i32-11+i321−i32-11+i321−i32
χ2611−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32
χ272222-1-1-10002222-1-1-10002222-1-1-1000-2-2-2-2111000-2-2-2-21110002222-1-1-1000-2-2-2-2111000
χ2822−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i3200022−1+i3−1−i3-11−i321+i32000-2-21−i31+i31−1+i32−1−i32000
χ2922−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i3200022−1−i3−1+i3-11+i321−i32000-2-21+i31−i31−1−i32−1+i32000
χ306-3000000006-3000000006-300000000-6300000000-63000000006-300000000-6300000000
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ321111111-1-1-11111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111111111-1-1-1
χ3311−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321+i32-11−i321+i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ3411−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321+i32-11−i321+i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32-11−i321+i32
χ3511−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321−i32-11+i321−i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ3611−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321−i32-11+i321−i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32-11+i321−i32
χ372222-1-1-10002222-1-1-10002222-1-1-1000-2-2-2-2111000-2-2-2-2111000-2-2-2-21110002222-1-1-1000
χ3822−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i3200022−1+i3−1−i3-11−i321+i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i32000-2-21−i31+i31−1+i32−1−i3200022−1+i3−1−i3-11−i321+i32000
χ3922−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i3200022−1−i3−1+i3-11+i321−i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i32000-2-21+i31−i31−1−i32−1+i3200022−1−i3−1+i3-11+i321−i32000
χ406-3000000006-3000000006-300000000-6300000000-6300000000-63000000006-300000000
χ4122222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ422222222-2-2-22222222-2-2-2-2-2-2-2-2-2-22220000000000000000000000000000000000000000
χ4322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-2-21−i31+i3-21−i31+i3-21−i31+i30000000000000000000000000000000000000000
χ4422−1+i3−1−i32−1+i3−1−i3-21−i31+i322−1+i3−1−i32−1+i3−1−i3-21−i31+i3-2-21−i31+i3-21−i31+i32−1+i3−1−i30000000000000000000000000000000000000000
χ4522−1−i3−1+i32−1−i3−1+i32−1−i3−1+i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-2-21+i31−i3-21+i31−i3-21+i31−i30000000000000000000000000000000000000000
χ4622−1−i3−1+i32−1−i3−1+i3-21+i31−i322−1−i3−1+i32−1−i3−1+i3-21+i31−i3-2-21+i31−i3-21+i31−i32−1−i3−1+i30000000000000000000000000000000000000000
χ474444-2-2-20004444-2-2-2000-4-4-4-42220000000000000000000000000000000000000000000
χ4844−2+2i3−2−2i3-21−i31+i300044−2+2i3−2−2i3-21−i31+i3000-4-42−2i32+2i32−1+i3−1−i30000000000000000000000000000000000000000000
χ4944−2−2i3−2+2i3-21+i31−i300044−2−2i3−2+2i3-21+i31−i3000-4-42+2i32−2i32−1−i3−1+i30000000000000000000000000000000000000000000
χ5012-60000000012-600000000-126000000000000000000000000000000000000000000000000
χ512222222222-2-2-2-2-2-2-2-2-2-200000000002222222222−2−2−2−2−2−2−2−2−2−200000000000000000000
χ522222222-2-2-2-2-2-2-2-2-2-222200000000002222222−2−2−2−2−2−2−2−2−2−222200000000000000000000
χ5322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-2-21−i31+i3-21−i31+i3-21−i31+i3000000000022ζ5−ζ23−ζ7+ζ132ζ5−ζ23−ζ7+ζ132ζ5−ζ23−ζ7+ζ13−2−2−ζ5+ζ23ζ7−ζ13−2−ζ5+ζ23ζ7−ζ13−2−ζ5+ζ23ζ7−ζ1300000000000000000000
χ5422−1+i3−1−i32−1+i3−1−i3-21−i31+i3-2-21−i31+i3-21−i31+i32−1+i3−1−i3000000000022ζ5−ζ23−ζ7+ζ132ζ5−ζ23−ζ7+ζ13−2−ζ5+ζ23ζ7−ζ13−2−2−ζ5+ζ23ζ7−ζ13−2−ζ5+ζ23ζ7−ζ132ζ5−ζ23−ζ7+ζ1300000000000000000000
χ5522−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-2-21+i31−i3-21+i31−i3-21+i31−i3000000000022−ζ7+ζ13ζ5−ζ232−ζ7+ζ13ζ5−ζ232−ζ7+ζ13ζ5−ζ23−2−2ζ7−ζ13−ζ5+ζ23−2ζ7−ζ13−ζ5+ζ23−2ζ7−ζ13−ζ5+ζ2300000000000000000000
χ5622−1−i3−1+i32−1−i3−1+i3-21+i31−i3-2-21+i31−i3-21+i31−i32−1−i3−1+i3000000000022−ζ7+ζ13ζ5−ζ232−ζ7+ζ13ζ5−ζ23−2ζ7−ζ13−ζ5+ζ23−2−2ζ7−ζ13−ζ5+ζ23−2ζ7−ζ13−ζ5+ζ232−ζ7+ζ13ζ5−ζ2300000000000000000000
χ574444-2-2-2000-4-4-4-4222000000000000022222222−2−2−2000−22−22−22−2222200000000000000000000000
χ5844−2+2i3−2−2i3-21−i31+i3000-4-42−2i32+2i32−1+i3−1−i3000000000000022222ζ5−2ζ23−2ζ7+2ζ13−2−ζ5+ζ23ζ7−ζ13000−22−22−2ζ5+2ζ232ζ7−2ζ132ζ5−ζ23−ζ7+ζ1300000000000000000000000
χ5944−2−2i3−2+2i3-21+i31−i3000-4-42+2i32−2i32−1−i3−1+i300000000000002222−2ζ7+2ζ132ζ5−2ζ23−2ζ7−ζ13−ζ5+ζ23000−22−222ζ7−2ζ13−2ζ5+2ζ232−ζ7+ζ13ζ5−ζ2300000000000000000000000
χ6012-600000000-12600000000000000000062−3200000000−62320000000000000000000000000000
χ612222222222-2-2-2-2-2-2-2-2-2-20000000000−2−2−2−2−2−2−2−2−2−2222222222200000000000000000000
χ622222222-2-2-2-2-2-2-2-2-2-22220000000000−2−2−2−2−2−2−22222222222−2−2−200000000000000000000
χ6322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-2-21−i31+i3-21−i31+i3-21−i31+i30000000000−2−2−ζ5+ζ23ζ7−ζ13−2−ζ5+ζ23ζ7−ζ13−2−ζ5+ζ23ζ7−ζ1322ζ5−ζ23−ζ7+ζ132ζ5−ζ23−ζ7+ζ132ζ5−ζ23−ζ7+ζ1300000000000000000000
χ6422−1+i3−1−i32−1+i3−1−i3-21−i31+i3-2-21−i31+i3-21−i31+i32−1+i3−1−i30000000000−2−2−ζ5+ζ23ζ7−ζ13−2−ζ5+ζ23ζ7−ζ132ζ5−ζ23−ζ7+ζ1322ζ5−ζ23−ζ7+ζ132ζ5−ζ23−ζ7+ζ13−2−ζ5+ζ23ζ7−ζ1300000000000000000000
χ6522−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-2-21+i31−i3-21+i31−i3-21+i31−i30000000000−2−2ζ7−ζ13−ζ5+ζ23−2ζ7−ζ13−ζ5+ζ23−2ζ7−ζ13−ζ5+ζ2322−ζ7+ζ13ζ5−ζ232−ζ7+ζ13ζ5−ζ232−ζ7+ζ13ζ5−ζ2300000000000000000000
χ6622−1−i3−1+i32−1−i3−1+i3-21+i31−i3-2-21+i31−i3-21+i31−i32−1−i3−1+i30000000000−2−2ζ7−ζ13−ζ5+ζ23−2ζ7−ζ13−ζ5+ζ232−ζ7+ζ13ζ5−ζ2322−ζ7+ζ13ζ5−ζ232−ζ7+ζ13ζ5−ζ23−2ζ7−ζ13−ζ5+ζ2300000000000000000000
χ674444-2-2-2000-4-4-4-42220000000000000−22−22−22−2222200022222222−2−2−200000000000000000000000
χ6844−2+2i3−2−2i3-21−i31+i3000-4-42−2i32+2i32−1+i3−1−i30000000000000−22−22−2ζ5+2ζ232ζ7−2ζ132ζ5−ζ23−ζ7+ζ1300022222ζ5−2ζ23−2ζ7+2ζ13−2−ζ5+ζ23ζ7−ζ1300000000000000000000000
χ6944−2−2i3−2+2i3-21+i31−i3000-4-42+2i32−2i32−1−i3−1+i30000000000000−22−222ζ7−2ζ13−2ζ5+2ζ232−ζ7+ζ13ζ5−ζ230002222−2ζ7+2ζ132ζ5−2ζ23−2ζ7−ζ13−ζ5+ζ2300000000000000000000000
χ7012-600000000-126000000000000000000−62320000000062−320000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.